...... but apparently if the aquahot also runs off the invertor they don't like to run at the same time.
It is highly unlikely that the AquaHot electric element draws 120 from the inverter. Nor will the A/C and laundry. The only high amp load that does draw from the inverter may be the microwave. A minute or two to heat something is OK. Longer times will draw down the battery fast.
The AquaHot will run on diesel with 12 volt house power. 120 is not needed.
The "trick" on 15 amps is to make sure the battery charger is not using more than it's "fair share". If batteries are discharged our "smart" inverter/chargers can assume they have a full range of power and will immediattly go to work at full speed to get the batteries back to a full charge state. On our Beaver that initial load could be as high at 20 or more amps. It would gradually taper off but on a 15 amp supply, it would trip the shore supply breaker in seconds. Inverter/Charger controls vary, but if you are on a 15 amp shore power, it is necessary to tell it your are through the control panel. When we were on 15 amps (and I elected to not use an external charger), I would set the onboard inverter/charger to 10 amps max.
Even with the 10 amp max, if I used the microwave it would add about 10 amps putting the 15 amp shore power breaker past its limit. You can stay on 15 amp hookups a long time. But, you can't use much of anything more than the TV because of the charger's "overhead".
If you draw down your batteries and don't tame your inverter/charger to something less than 15 amps, you may have continuing trouble every time you restore the external 15 amps. The supply breaker will continue to trip when the charger demands its initial load and you will never get the house batteries up. Continued discharge may draw them down to a point of them being permanently damaged.